Closure caps of the abovementioned generic type are generally known. They permit the dispensing of liquid or powdered spray product by pressing in one or more flexible walls of the container. Due to the so-called memory character of the walls, the latter have the tendency to resume their original position when the container is released. Associated with this is a sucking-in of air through the dispensing opening of the closure cap. This effect may entail disadvantages, if for example the pack equipped with the closure cap is used for medical purposes in which a curative or remedial preparation has to be dispensed by introducing the front end of the closure cap, containing the dispensing opening, into a body orifice. In this case the possibility cannot be ruled out that, while the closure cap with its dispensing opening is still inserted in the body orifice, fluid in the body orifice is sucked in by the readmission of air into the container and leads to a contamination of the product contained in the container. For instance, for combating colds, so-called nasal spray systems are known in which, after spraying the spray into the nose, nasal secretion is sucked in by the readmission of air to the container and, as a result, the product is contaminated.